Complementarity and the uncertainty relations

Björk, Gunnar; Söderholm, Jonas; Trifonov, Alexei; Tsegaye, T.; Karlsson, Anders

doi:10.1103/physreva.60.1874

Cited by 53 publications

(80 citation statements)

References 31 publications

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“…Some examples are: (i) the quantum-mechanical result for the correlation among two distant particles in an entangled state, rather than a weaker correlation limited by the assumption of Local Realism [110][111][112], (ii) the perturbation expansion of the Schrödinger equation [113,114] leading to the two dimensional spinor representation with the exponential decay law, (iii) the unitarity relations [115], (iv) the complementarity of CP parity and strangeness [116][117][118], (v) that the K 0 and the K 0 from φ decay are exact CPT conjugates [84], (vi) the conservation of the purity of states of isolated particles, manifested by the long time coherence of the kaon matter wave [65,66]. On the last subject, data from the CPLEAR Collaboration in combination with earlier data from the CERN-HEIDELBERG Collaboration achieve a sensitivity of ≈ 10 −21 GeV.…”

Section: Discussionmentioning

confidence: 99%

“…(234) tells us that we have zero knowledge of whether the particle came originally from the noth pole, or from the south pole. For more detailed considerations, see for instance [116][117][118]. From the left, the 200 MeV/c p beam delivered by LEAR enters the magnet along its axis, and through a thin scintillator (Beam monitor) reaches a pressurized hydrogen gas target (T) where antiprotons stop and annihilate.…”

Section: Neutral Kaons and Optical Interferencementioning

confidence: 99%

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The fundamental symmetries in the neutral kaon system—a pedagogical choice

Fidecaro

Gerber²

2006

Rep. Prog. Phys.

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During the recent years experiments with neutral kaons have yielded remarkably sensitive results which are pertinent to such fundamental phenomena as CPT invariance (protecting causality), time-reversal invariance violation, coherence of wave functions, and entanglement of kaons in pair states. We describe the phenomenological developments and the theoretical conclusions drawn from the experimental material. An outlook to future experimentation is indicated.

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Section: Discussionmentioning

confidence: 99%

Section: Neutral Kaons and Optical Interferencementioning

confidence: 99%

The fundamental symmetries in the neutral kaon system—a pedagogical choice

Fidecaro

Gerber²

2006

Rep. Prog. Phys.

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“…For this particular example of two-beam interferometry some other operational duality relations have been examined before being computed directly in terms of the outputs of a noisy joint measurement of the corresponding observables [3,4]. This sort of approach focuses on the outcomes w of the measurement, disregarding most of the information contained in ⌬͑w͒.…”

Section: B Operational Approachmentioning

confidence: 99%

“…In Refs. [1][2][3][4][5][6][7][8] the interested reader can find some examples concerning formal definitions [1], quantitative evaluation [2][3][4], experimental observations [5][6][7], and investigation of its physical origin [8].…”

Section: Introductionmentioning

confidence: 99%

Operational approach to complementarity and duality relations

Luis

2004

Phys. Rev. A

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We present a fully operational and consistent approach to complementarity. In contrast to previous approaches, in this proposal the duality relations emerge exclusively from the outcomes of simultaneous measurements performed on every run of the experiment and under the same experimental conditions. This can be done without assuming any definite relationship between the measurement performed and the complementary observables being studied.

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“…This experiment uses nuclear magnetic resonance techniques to entangle the spin states of the 13 C nucleus with those of the 1 H nucleus in a chloroform molecule, 13 CHCl 3 . The 13 C nucleus is taken to be the object system (o), while the 1 H nucleus serves as the probe (p).…”

mentioning

confidence: 99%

Uncertainty reconciles complementarity with joint measurability

Busch

Shilladay

2003

Phys. Rev. A

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The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary observables is proposed. The measured observables are represented as positive operator valued measures (POVMs), whose intrinsic fuzziness parameters are found to satisfy an intriguing pay-off relation reflecting the complementarity. At the same time, this relation represents an instance of a Heisenberg uncertainty relation for measurement imprecisions. A model-independent consideration show that this uncertainty relation is logically connected with the joint measurability of the POVMs in question. Ever since the inception of quantum mechanics, the principles of complementarity and uncertainty have been fundamental issues in the debate about an adequate understanding of this theory. Usually these principles are understood as expressions of limitations on the preparation and measurement of quantum systems; these limitations arise from the fact that in quantum mechanics there are many pairs of non-commuting observables. Complementarity is the mutual exclusiveness of preparing or measuring sharp values of certain pairs of non-commuting observables [1]. The uncertainty relation gives a more quantitative expression of complementarity: the more sharply the value of one quantity is defined or determined, the less sharply the other quantity can be defined or determined.Here we will develop a somewhat more positive view of the uncertainty relation: in one version, this relation can be understood as a pay-off inequality between the measurement imprecisions in joint unsharp measurements of a complementary pair of observables. This interpretation is introduced in Heisenberg's seminal paper of 1927 [2] but at that time and for many decades afterwards, it was not possible to formally distinguish it from the well-known relation for variances of sharp position and momentum, and thus it got conflated with this latter version.It was only after the introduction of positive operator valued measures (POVMs) into physics in the 1960s and 1970s (first by Ludwig and somewhat later by Davies, * Electronic address: p.busch@hull.ac.uk † Electronic address: c.r.shilladay@maths.hull.ac.ukHelstrom, Holevo, and others, for a survey, see [3]) that a notion of joint measurement of non-commuting observables could be formulated in the Hilbert space formalism of quantum mechanics. This has then been used to study models of joint measurement schemes for position and momentum, spin components and other quantities, which all led to some form of measurement uncertainty relation. This development is reviewed in [3]. In this letter we propose a new, realizable scheme of a joint measurement of complementary spin-1/2 components (or any pair of 'qubit' observables); we will find a novel pay-off relation for measures of unsharpness associated with the observables involved, and we will show that this form of Heisenberg measurement un...

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Complementarity and the uncertainty relations

Cited by 53 publications

References 31 publications

The fundamental symmetries in the neutral kaon system—a pedagogical choice

The fundamental symmetries in the neutral kaon system—a pedagogical choice

Operational approach to complementarity and duality relations

Uncertainty reconciles complementarity with joint measurability

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